Lab-in-a-Box
Experiment 16: A Differentiator Circuit
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Pledge: _____________________
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______________________
Date: ______________________
Procedure
Analysis:
1. Derive the input-to-output relationship [Eq (1)] of the amplifier circuit shown in Figure 1. Which trim
pot is required such that the circuit may be adjusted to have a unity scaling factor for a sine wave at
1500 Hz? Note: for most effective operation, the desired resistance should be near the middle of the
range of the trim pot.
R1
V-
uA741
2
-
V-
C1
4
9Vdc
OS1
0.1u
VOFF = 0
VAMPL = 5
FREQ = 500
+
U1
OS2
7
3
V3
V+
OUT
V+
9Vdc
1
6
5
R2
10k
Figure 1: An ideal differentiating op amp circuit.
2. Calculate the component values required such that the differentiator circuit of Figure 2 will have unity
gain at 1500 Hz (  R1C1  1 ) and will have cut-off or corner frequencies of 3000 Hz (  R2C1  1 )and
5000 Hz (  R1C2  1 ) for the series resistor R1 and the feedback capacitor C2, respectively. Use a 0.1
μF capacitor for C1. Round your remaining component values to the nearest components available in
your kit (see Appendix A). Which trim pot is required to achieve the desired amplifier performance?
Note: the cutoff frequencies do not correspond to -3 dB frequencies.
C2
R1
V-
C1
uA741
2
-
V-
R2
4
9Vdc
OS1
0.1u
3
+
U1
V3
OS2
7
VOFF = 0
VAMPL = 5
FREQ = 1500
V+
OUT
V+
9Vdc
1
6
5
R3
10k
Figure 2: A practical differentiator circuit.
Modeling:
3. Using the component values determined in step 1, model the circuit of Figure 1 in PSpice for a 5.0 V
amplitude sine wave input signal with frequencies (f) varying from 500 to 3000 Hz in steps of 500
Hz. For each frequency, adjust the value of R1 to obtain an output signal of 5.0 V. Hint: instructions
for sweeping a pot in PSpice may be found on the book WWW site at
http://www.wiley.com/college/Hendricks. Record screen shots of your schematic and of your
PSpice simulation results for 500 Hz. Also record in a table the value of R1 at each frequency that
yields unity gain for the PSpice simulation.
4. Using your choice of scientific graphing program (e.g., Excel or MATLAB), plot a graph (in log-log
space) of the value of R1 determined in step 3 versus f. Do not plot data points, but only plot a line
joining the data points. Save your graph for use in step 16. Examine the MALAB file in Appendix
D.1 for an example of easy way to plot such data in MATLAB. Background information may be
found in both Stinson and Dodge (2004) for Excel and in Hanselman and Littlefield (2005) for
MATLAB.
5. Do your results agree with the condition  R1C1  1 ? Hint: solve this expression for ω and show that
the data should be a straight line of slope -1 when plotted in log-log space. Plot this line on your
graph drawn in step 4.
6. Repeat steps 3 through 5 for the circuit in Figure 2 using the component values computed in step 2.
Save your graph for use in step 25.
7. What effect do R2 and C2 have on the performance of the circuit as compared to the circuit of Figure 1
in the frequency range 500  f  3500 Hz?
Measurements: Ideal differentiator
8. Construct the differentiator amplifier circuit shown in Figure 1. Notes: (a) Be careful to use the center
terminal and one end terminal of the trim pot. Following the “good practice” note in Section 2.11, be
sure to connect the unused terminal of the trim pot to pin 2 (the wiper) of the trim pot. (b) Use the
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ANDY board function generator with the shape set to SIN and the OFFSET set to zero for the input
signal. Make sure your sine wave amplitude is not zero! (c) Although the circuit diagram calls for a
μ741 op amp, use the LF 356 called for in the bill of materials.†
9. Connect the output of the function generator to the 10 attenuator of channel 1 (green) to the
oscilloscope and the output of the op amp to the 10 attenuator of channel 2 (red).
10. Adjust the frequency of the function generator (green trace) to produce a 500 Hz sine wave. Hint:
You may observe the signal frequency in the oscilloscope mode or you may change the view by
pressing the “Frequency Analysis” tab at the top of the oscilloscope screen. In the spectrum view, you
should see a single peak at the frequency of the source. There is a box below the spectrum window
that is labeled “main frequency” which will provide a numerical value for the frequency. We
generally find that it is easiest to set a desired frequency in the Spectrum mode.
11. Adjust the amplitude of the function generator to 5.0 V. Remember that you are using the 10
attenuator, so you should read 0.5 V on the oscilloscope screen and interpret that as 5.0 V.
12. Observe the output of the op amp on the oscilloscope (red trace). It should be a sine wave of the same
frequency as the function generator but with a phase shift of 90o. Verify the frequency in either the
“Oscilloscope” or the “Spectrum” mode of the oscilloscope. Record screen shots to document your
results. Measure the phase shift of the two signals using the methodology described in the
Background section of Experiment 20.
13. Adjust the trim pot R1 to produce an output signal with a 5.0 V amplitude.
14. Remove the trim pot from the circuit and use your DMM to measure the resistance between the same
two terminals as were wired in the experiment. Be sure to turn off the ANDY board before removing
the pot. Be careful to not change the setting of the trim pot.
15. Repeat steps 10 though 14 for frequencies of 1000 Hz to 3000 Hz in steps of 500 Hz. Record a screen
shot for the signal at 1500 Hz and prepare a table of the R1 resistance measurements vs. frequency.
Suggestion: Examine the resistor values for unity gain at each frequency computed in step 3 before
attempting to adjust the trim pot. This will give you a feel for how to adjust the pot. It is easy to miss
the target resistance if you adjust the pot too quickly.
16. Plot the potentiometer resistance vs. frequency data obtained in step 15 on the graph created in step 4.
Plot only the data points.
17. Do your experimental observations agree with your PSpice models and with the derivation presented
in the Background? Comment and/or explain.
Measurements: Practical Differentiator
18. Turn off the ANDY board and add the components R2 and C2 to create the circuit shown in Figure 2.
19. Adjust the frequency of the function generator (green trace) to produce a 500 Hz sine wave.
20. Adjust the amplitude of the function generator to 5.0 V.
21. Observe the output of the op amp on the oscilloscope (red trace). It should be a sine wave of the same
frequency as the function generator but with a phase shift of 90o. Verify the frequency in either the
“Oscilloscope” or the “Spectrum” mode of the oscilloscope. Record screen shots to document your
results. Confirm that the phase shift is 90o.
22. Adjust the trim pot R1 to produce an output signal with a 5.0 V amplitude.
†
The PSpice model for the LF356 op amp, available at the National Semiconductor WWW site, has a large number
of nodes and the circuits of Figures 1 and 2 will fail in the demo version of PSpice. The model for the μ741 is
simpler and and is adequate for the purposes of this experiment.
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23. Remove the trim pot from the circuit and use your DMM to measure the resistance between the same
two terminals as were wired in the experiment. Be careful to not change the setting of the trim pot. Be
sure to turn off the ANDY board before removing the pot.
24. Repeat steps 19 though 23 for frequencies of 1000 Hz to 3000 Hz in steps of 500 Hz. Record a screen
shot for the signal at 1500 Hz and prepare a table of the R1 resistance measurements vs. frequency.
25. Plot the potentiometer resistance vs. frequency data obtained in step 24 on the graph created in step 6.
Plot only the data points.
26. Do your experimental observations agree with your PSpice models and with the derivation presented
in the Background? Comment on the effect of these components on the performance of the circuit.
Last Revision
4.0: 11/23/2006
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